1. PPT6: Advanced Geometric Algorithms
CAP 6736
Geometric Modeling
PPT6: Advanced Geometric Algorithms
PPT and video are due no later than February 22
Submit to:
This template file is just an outline of the presentation
that you need to complete. Additional pages may
be necessary to fully explore the topic above.
Each page should contain adequate text as well
as illustrations. You are free to use all publicly
available information (text as well as graphics) as long as
the sources are properly acknowledged.

2. Team members’ contributions
Member [name]:

3. Part I: Technical details
For this part you will need an equation editor. You may use:
MS equation editor,
MathType,
LaTeX, or
Handwritten equations if all else fails

4. Point Projection Suggested content: Point projection to curves
Math a basic algorithm

5. Point Projection Suggested content: Point projection to curves
Conditions for convergence

6. Point Projection Suggested content: Point projection to surfaces
Math a basic algorithm

7. Point Projection Suggested content: Point projection to curves
Conditions for convergence

8. Surface Tangent Vector Inversion
Suggested content:
Surface tangent inversion
Math a basic algorithm

9. Projection of Curves Suggested content: Project curves to planes
Parallel case: projected control points

10. Projection of Curves Suggested content: Project curves to planes
Perspective case
projected control points
new weights

11. Projection of Surfaces
Suggested content:
Project surfaces to planes
Parallel and perspective cases

12. Transformations Suggested content:
Transformation of curves and surfaces
rotation, scaling, shear
translation
projections

13. Reparametrization Suggested content: Reparametrization of curves
General formula
A detailed example

14. Reparametrization Example
Suggested content:
Reparametrization example of Bezier
Use derivatives to compute control points

15. Linear Parametrization Function
Suggested content:
Reparametrization example: linear functions

16. Reparametrization of NURBS Curves
Suggested content:
Reparametrization of NURBS curves
General formula
Algorithm sketch

17. Reparametrization of NURBS Curves
Suggested content:
Reparametrization examples
Use different functions

18. Better Circle Weights Suggested content:
Better circle weights using reparametrization

19. Reparametrization with Linear Rationals
Suggested content:
Reparametrization with linear rational functions
General formula and algorithm sketch

20. Reparametrization with Linear Rationals
Suggested content:
Reparametrization curve examples
Reparametrization surface examples

21. Making End Weights Equal
Suggested content:
Making end weights as reparametrization

22. Curve Reversal
Suggested content:
Curve reversal as reparametrization

23. Surface Reversal Suggested content:
Surface reversal as reparametrization

24. B-spline to Power Basis Conversion
Suggested content:
B-spline curve to power basis conversion
decompose into Bezier
convert Bezier
reparametrize to power basis

25. B-spline to Power Basis Conversion
Suggested content:
B-spline surface to power basis conversion
decompose into Bezier
convert Bezier
reparametrize to power basis

26. Power Basis to B-spline
Suggested content:
Power basis to B-spline curve conversion
reparametrize power basis segments
convert power basis to Bezier
form B-spline from Bezier
remove excess knots

27. Power Basis to B-spline
Suggested content:
Power basis to B-spline surface conversion
reparametrize power basis segments
convert power basis to Bezier
form B-spline from Bezier
remove excess knots

28. Part II: Design examples

29. Design Examples Suggested content:
Add design examples: images and/or videos
Give credit to the designers

30. Part III: GM lab
For this part of the assignment you may use an existing system,
such as Blender, or write the code and visualize the result
using graphics tools like Processing.

31. Geometric Modeling Lab
Suggested project:
Use point projection to curves and surfaces
Find interesting applications